{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4: A visual proof that neural nets can compute any function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Two caveats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universality with one input and one output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Many input variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 1 ([link](http://neuralnetworksanddeeplearning.com/chap4.html#problem_863961)): approximate any arbitrary function with just a single hidden layer\n",
    "\n",
    "Let's consider only 2 input variables, $x$ and $y$, and a real-valued function.\n",
    "\n",
    "First, why did we need that second hidden layer before, instead of simply adding our tower functions together to approximate $\\sigma^{-1} \\circ f(x,y)$ for the weighted input of our last neuron, giving $f(x,y)$ as the output of our network?\n",
    "\n",
    "The reason is that we need to get rid of the plateaus associated with each tower, with a bias of $-3 \\frac h 2$ (or $(-m+ \\frac 1 2)h$, in $m$ dimensions):\n",
    "\n",
    "![img/tower_and_plateaus.png](img/tower_and_plateaus.png)\n",
    "\n",
    "Since the towers have different heights, we have to define different biases for different towers, and therefore a single output neuron won't be enough: we need a second hidden layer. How do we circumvent this limitation?\n",
    "\n",
    "Following Nielsen's hints:\n",
    "\n",
    "**(a) it's possible to get step functions not just in the $x$ or $y$ directions, but in an arbitrary direction**\n",
    "\n",
    "We already know how to get step functions in the $x$ direction or $y$ direction (going through any couple of points $(x_0, y_0)$ by adjusting the bias). What about a step function along the line going through $(0, y_0)$ with an angle to the absciss $\\alpha \\in \\mathopen] -\\pi, \\pi \\mathclose[ \\backslash \\{ -\\pi/2, \\pi/2\\}$?\n",
    "\n",
    "The corresponding line equation is $y = x \\tan \\alpha + y_0$.\n",
    "\n",
    "We fix $w_x$ to be a large value, and want to determine $w_y$ and $b$ such that the weighted input $z = w_x x + w_y y + b$ is equal to 0 (so the output activation will be $0.5$) on the line $y = x \\tan \\alpha + y_0$.\n",
    "\n",
    "This translates to:\n",
    "\n",
    "$$\\forall x \\in \\mathbb{R}, w_x x + w_y x \\tan \\alpha + w_y y_0 + b = 0$$\n",
    "\n",
    "$$\\forall x \\in \\mathbb{R}, \\left( w_x + w_y \\tan \\alpha \\right) x + \\left( w_y y_0 + b \\right) = 0$$\n",
    "\n",
    "Which implies, since $\\left( w_x + w_y \\tan \\alpha \\right)$ and $\\left( w_y y_0 + b \\right)$ are constant, that:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "  \\left\\{ \n",
    "    \\begin{array}{ll} \n",
    "      w_x + w_y \\tan \\alpha &= 0 \\\\\n",
    "      w_y y_0 + b &= 0\n",
    "    \\end{array}\n",
    "  \\right.\n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "  \\iff \\left\\{ \n",
    "    \\begin{array}{ll} \n",
    "      w_y &= - \\frac{w_x}{\\tan \\alpha} \\\\\n",
    "      b &= \\frac{y_0 w_x}{\\tan \\alpha}\n",
    "    \\end{array}\n",
    "  \\right.\n",
    "\\end{eqnarray}\n",
    "\n",
    "Then for every point $(x, y)$ at a distance $d$ below the line, with a little geometry we can compute that $y = (x - d) \\tan \\alpha + y_0$, so the value of the sigmoid function on this point is:\n",
    "\n",
    "$$\\sigma\\left( w_x x - \\frac{w_x}{\\tan \\alpha} ((x-d) \\tan \\alpha + y_0) + \\frac{y_0 w_x}{\\tan \\alpha} \\right) = \\sigma(w_x d)$$\n",
    "\n",
    "So we have a good step function. Let's plot one ($w_x = 10, \\alpha = \\pi / 20, y_0 = 1$):\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot(x, y, zs):\n",
    "    \"\"\"Plot zs as a function of x and y\"\"\"\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    Z = zs.reshape(X.shape)\n",
    "    ax.plot_surface(X, Y, Z)\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_ylabel('y')\n",
    "    ax.set_zlabel('z')\n",
    "    plt.show()\n",
    "\n",
    "def step(wx, x, y, y0, alpha):\n",
    "    wy = - wx / np.tan(alpha)\n",
    "    b = y0 * wx / np.tan(alpha)\n",
    "    return sigmoid(wx*x + wy*y + b)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "wx = 100  # any large value\n",
    "alpha = np.pi / 20  # rad\n",
    "y0 = 1  # the line will pass through the point (0, y0)\n",
    "\n",
    "x = y = np.arange(-3.0, 3.0, 0.05)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "zs = np.array([step(wx, x, y, y0, alpha) for x, y in zip(np.ravel(X), np.ravel(Y))])\n",
    "plot(x, y, zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we just have to add 2 of these step functions with different $y_0$ and opposite weights to get a bump function.\n",
    "\n",
    "Again, a little geometry shows that to create a bump of angle $\\alpha$ to the absciss, of width $R$ and centered around $(x_0, y_0)$, we need to subtract step functions both of angle $\\alpha$ and going through $(0, y_0 - x_0 \\tan \\alpha + \\frac{R}{2\\cos\\alpha})$ and $(0, y_0 - x_0 \\tan \\alpha - \\frac{R}{2\\cos\\alpha})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bump(x, y, wx, x0, y0, alpha, R):\n",
    "    \"\"\"Bump function of width R, angle alpha to the absciss,\n",
    "    centered around (x0, y0).\n",
    "    alpha must be in [0, 2pi[.\"\"\"\n",
    "    if alpha == 0 or alpha == np.pi:\n",
    "        return ybump(x, y, wx, x0, y0, R)\n",
    "    if alpha == np.pi / 2 or alpha == 3 * np.pi/2:\n",
    "        return xbump(x, y, wx, x0, y0, R)\n",
    "    \n",
    "    wy = - wx / np.tan(alpha)\n",
    "    y01 = y0 - x0 * np.tan(alpha) + R / (2 * np.cos(alpha))\n",
    "    y02 = y0 - x0 * np.tan(alpha) - R / (2 * np.cos(alpha))\n",
    "    \n",
    "    if alpha > np.pi:\n",
    "        y01, y02 = y02, y01  # to prevent a negative bump\n",
    "    \n",
    "    b1 = y01 * wx / np.tan(alpha)\n",
    "    b2 = y02 * wx / np.tan(alpha)\n",
    "    return sigmoid(wx*x + wy*y + b1) - sigmoid(wx*x + wy*y + b2)\n",
    "\n",
    "def xbump(x, y, w, x0, y0, R):\n",
    "    \"\"\"Bump function of width R, centered around (x0, y0),\n",
    "    along the x axis.\"\"\"\n",
    "    return sigmoid(w*(x - x0 + R/2)) - sigmoid(w*(x - x0 - R/2))\n",
    "\n",
    "def ybump(x, y, w, x0, y0, R):\n",
    "    \"\"\"Bump function of width R, centered around (x0, y0),\n",
    "    along the y axis.\"\"\"\n",
    "    return sigmoid(w*(y - y0 + R/2)) - sigmoid(w*(y - y0 - R/2))\n",
    "\n",
    "wx = 100  # any large value\n",
    "alpha = np.pi/20 # rad\n",
    "R = 1\n",
    "x0 = 10\n",
    "y0 = -5\n",
    "\n",
    "x = np.arange(7, 13, 0.05)\n",
    "y = np.arange(-8, -2, 0.05)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "zs = np.array([bump(x, y, wx, x0, y0, alpha, R) for x, y in zip(np.ravel(X), np.ravel(Y))])\n",
    "plot(x, y, zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To adjust the height of our bump function, we'll use the weights going from those 2 neurons to the output neuron, which doesn't require a second hidden layer.\n",
    "\n",
    "**(b) by adding up many of the constructions from part (a) it's possible to approximate a tower function which is circular in shape, rather than rectangular**\n",
    "\n",
    "Suppose we want a circular tower of diameter $R$ and height 1 (then constructing a tower of any height will be easy), centered in the point $(x_0, y_0)$. We'll use a large number $m$ of the previous bump functions of height $\\frac 1 m$, of width $R$ and uniformly distributed angles $\\alpha$ to the absciss: $\\alpha \\in \\left\\{ 0, 1 \\times \\frac{2\\pi}{m}, 2 \\times \\frac{2\\pi}{m}, \\ldots, (m-1) \\times \\frac{2\\pi}{m} \\right\\}$.\n",
    "\n",
    "Here's an example with $m = 30$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bumps(x, y, wx, x0, y0, R, m):\n",
    "    \"\"\"Return a sum of m bump functions centered around (x0, y0)\n",
    "    and with angles uniformly distributed in [0, 2pi[\"\"\"\n",
    "    total = 0\n",
    "    alphas = [i*2*np.pi/m for i in range(m)]\n",
    "    for alpha in alphas:\n",
    "        total += bump(x, y, wx, x0, y0, alpha, R)\n",
    "    return total/m\n",
    "\n",
    "wx = 100  # any large value\n",
    "R = 1\n",
    "x0 = 10\n",
    "y0 = -5\n",
    "m = 30\n",
    "\n",
    "x = np.arange(7, 13, 0.05)\n",
    "y = np.arange(-8, -2, 0.05)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "zs = np.array([bumps(x, y, wx, x0, y0, R, m) for x, y in zip(np.ravel(X), np.ravel(Y))])\n",
    "plot(x, y, zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the limit as $m \\rightarrow +\\infty$, we will have a cylinder of height 1 and diameter $R$, surrounded by a function proportional to the fraction of angles having activated the considered point. This function will only depend on its distance $d$ to the point $(x_0, y_0)$, not its precise coordinates.\n",
    "\n",
    "One can show (with a drawing and some geometry) that this fraction is $\\frac{4}{\\pi} \\arctan \\frac{R}{2d}$.\n",
    "\n",
    "This means that as $m \\rightarrow +\\infty$, we tend toward this function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def limit(x, y, x0, y0, R):\n",
    "    \"\"\"Limit function of our approximation procedure\"\"\"\n",
    "    d = np.sqrt((x - x0)**2 + (y - y0)**2)\n",
    "    if 2*d <= R:\n",
    "        return 1\n",
    "    else:\n",
    "        return 4 / np.pi * np.arctan(R/(2*d))\n",
    "\n",
    "R = 1\n",
    "x0 = 10\n",
    "y0 = -5\n",
    "\n",
    "x = np.arange(7, 13, 0.05)\n",
    "y = np.arange(-8, -2, 0.05)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "zs = np.array([limit(x, y, x0, y0, R) for x, y in zip(np.ravel(X), np.ravel(Y))])\n",
    "plot(x, y, zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c) using these circular towers, it's possible to approximate an arbitrary function**\n",
    "\n",
    "TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extension beyond sigmoid neurons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 2 ([link](http://neuralnetworksanddeeplearning.com/chap4.html#problems_963556)): universality of ReLU neurons\n",
    "\n",
    "Recall that a rectified linear unit (ReLU) neuron with weighted input $z$ returns an activation equal to $\\max(0, z)$:\n",
    "\n",
    "![img/relu.png](img/relu.png)\n",
    "\n",
    "These neurons don't satisfy the condition of a finite limit as $z \\rightarrow + \\infty$.\n",
    "\n",
    "However, we can find an adapted proof of universality for them.\n",
    "\n",
    "We'll only need to show that one can compute a step function in 1 dimension with 2 ReLU neurons (when only 1 sigmoid neuron was needed), then the remaining of the proof in chapter 4 will apply.\n",
    "\n",
    "Consider an input $x$. We have two ReLU neurons of parameters $(w_1, b_1)$ and $(w_2, b_2)$.\n",
    "\n",
    "Suppose we want a step at absciss $x = s$, of height $h$.\n",
    "\n",
    "Take $w_1$ to be a large value, and $w_2 = w_1$.\n",
    "\n",
    "We'll subtract one function from the other, the only difference between them being a tiny offset making our step function. More specifically, we want the first neuron to begin growing at $x = s$, i.e. $w_1 s + b_1 = 0$. So set $b_1 = - w_1 s$.\n",
    "\n",
    "Now we want a height $h$, knowing that our first neuron output grows at a speed of $w_1$. This means we must compensate it beginning at $x = s + \\frac{h}{w_1}$. Therefore we want $w_2 \\left( s + \\frac{h}{w_1} \\right) + b_2 = 0$, i.e. $b_2 = - w_1 s - h$.\n",
    "\n",
    "Finally, weigh the output of the first neuron at 1, and the output of the second one at -1. That's it, we've got a step function in the limit as $w_1 \\rightarrow + \\infty$.\n",
    "\n",
    "Demo with $w_1 = 10, s = 2, h = 3$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "def step(w1, s, h, x):\n",
    "    return first_relu(w1, s, h, x) - second_relu(w1, s, h, x)\n",
    "\n",
    "def first_relu(w1, s, h, x):\n",
    "    b1 = - w1 * s\n",
    "    return relu(w1 * x + b1)\n",
    "\n",
    "def second_relu(w1, s, h, x):\n",
    "    w2 = w1\n",
    "    b2 = - w1 * s - h\n",
    "    return relu(w2 * x + b2)\n",
    "\n",
    "def relu(x):\n",
    "    return max(x, 0)\n",
    "\n",
    "w1 = 10  # any large value\n",
    "s = 2  # absciss of the beginning of the step\n",
    "h = 3  # height of the step\n",
    "\n",
    "X = np.arange(-1.0, 5.0, 0.05)\n",
    "Y1 = np.array([first_relu(w1, s, h, x) for x in X])\n",
    "Y2 = np.array([- second_relu(w1, s, h, x) for x in X])\n",
    "Y = np.array([step(w1, s, h, x) for x in X])\n",
    "\n",
    "plt.ylim(bottom=-5, top=5)\n",
    "plt.plot(X, Y1, label=\"First ReLU\")\n",
    "plt.plot(X, Y2, label=\"Second ReLU (negatively weighted)\")\n",
    "plt.plot(X, Y, label=\"Sum: step function\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3: non-universality of linear neurons\n",
    "\n",
    "Linear neurons ($s(z) = z$) don't satisfy the finite limits as $z \\rightarrow - \\infty$ and $z \\rightarrow + \\infty$.\n",
    "\n",
    "In a neural network made of linear neurons, each neuron only ever computes a weighted combination of the outputs of the neurons of the previous layers plus a bias: $z_j^l = \\sum\\limits_k w_{jk}^l a_k^{l-1} + b_j^l$.\n",
    "\n",
    "The output of the first layer will be linear in the input for each neuron. Then the weighted inputs (and so the outputs) of all neurons in the second layer will be linear, etc. Our network will only ever be able to compute linear functions.\n",
    "\n",
    "Linear neurons can't therefore be used to do universal computation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixing up the step functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  }
 ],
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